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1. Find the derivatives of the following:

a. [pic]

b. [pic]

c. [pic]

2. You should be able to get the derivatives of the other three inverse trig functions quite quickly. (Recall how the derivatives of the trig functions and the derivatives of the co- trig functions are related.)

3. What is the slope of y = 2x – 3?

4. What is the inverse of the equation from #3?

5. What is the slope of the line from #4?

6. Find the derivative of f(x) = x2.

7. Find the derivative of g(x) = [pic].

8. What is the relationship between f and g? (Hint: read the title of the sheet.)

9. Name 5 “pretty” points that are on f (use positive integers).

10. Use your 5 “pretty” points from f to name 5 “pretty” points on g.

11. Find the value of the derivative of f at your 5 pretty points.

12. Find the value of the derivative of g at your 5 pretty points.

13. What’s the point? Write it down!

14. A property of a function and its inverse is that [pic] (meaning they undo each other). Differentiate this equation and solve for the derivative of [pic].

15. Suppose that f(2) = 3 and [pic]. Can you find the value of the derivative of [pic]at

x = 2, 3, and 4? Explain. Find.

INVERSE CLASSWORK

Find the derivatives of the following:

1. cos-1(2x) [pic] 2. sin-1(1/x) [pic]

3. tan-1(ex) [pic] 4. cot-1([pic]) [pic]

5. sec-1(8) 0 5. csc-1(x2) [pic]

6. Use the following table to find the following:

|x |f (x) |f ((x) |

|0 |1 |1.3 |

|1 |2 |2.6 |

|2 |6 |3.9 |

|3 |8 |5.6 |

a. f -1(8) 3

b. (f –1)'(6) 0.256

c. f ((2) 3.9

d. (f –1)((2) 0.38

7. Let f be the function defined by f(x) = 2x + ex. If g(x) = [pic]for all x and the point

(0, 1) is on the graph of f, what is the value of g '(1)?

[pic]

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